The project began by asking: what is observable in quantum gravity and how does it relate to observable properties from general relativity in a classical regime? Any operational approach to quantum gravity must face this question if intending to connect with bottom-up approaches that aim to quantise gravity directly. The key result was that generic observables in gravity feature a complicated non-differentiable behaviour, due to the presence of chaos in general relativity. Strong repercussions were shown: a quantum theory encoding these observables and ultimately connecting with general relativity in a classical limit must be based on a modified method of quantisation. The article, published in Phys. Lett. B, also proposes how, thereby suggesting a solution to a long-standing problem in quantum gravity. This investigation significantly extended the project proposal: it addressed a question that becomes crucial in the context of the semiclassical limit of quantum gravity where it bears on information flow, encoded in observables, and thus directly on an informational network approach. The fellow presented this work in various talks.
In parallel, the work on deriving the Lorentz transformations of special relativity from operational consistency conditions on a quantum communication protocol for reference frame synchronisation was completed and published in New Journal of Physics (selected as an NJP highlights). The importance of this work was to derive basic space-time structure from the communication relations between observers and without putting any such structure in by hand. Throughout the fellowship, work continued on this topic by generalising this result to a reconstruction of the Poincare group, which is a prerequisite for a Minkowski space reconstruction from communication relations. The fellow also presented these works in several workshops.
In a spin-off, the fellow and collaborators put forward, using a special mix of arguments from quantum information and renormalisation in quantum gravity, the surprising possibility that the local linearity of space-time might ultimately be a consequence of the linearity of probabilities. This part addresses all three main objectives of the proposal and calls for further research. This was published as an invited contribution to a special edition of Journal of Physics A "emerging talents".
A key aspect of the programme was to extend the ideas for an informational approach to quantum gravity underlying the proposal to a consistent conceptual and technical road map that is concrete enough to be followed by further projects. The fellow laid down such a road map, clarifying that such an informational approach will necessarily be a top-down approach, starting from the known physics and going down in scale, to complement bottom-up efforts starting at the Planck scale and doing the opposite. This road map was published as an invited chapter of the proceedings of DICE 2016 and was also discussed in talks by the fellow.
A main effort was to follow this road map with concrete investigations. The first question studied is as follows. The usual explanations for the emergence of a classical world from within quantum theory rely on the assumption of external structures, not least a space-time. If spatiotemporal structures, however, are not an input but, instead, shall emerge from the information flow within a quantum network, how can the emergence of a classical macro-reality be explained without external structures? The answer to this question requires relational degrees of freedom (as in general relativity) and builds on a coarse-grained information exchange in the network caused by universality and monogamy of entanglement. The second question studied is how one can extract geometric information from the quantum correlations (encoding the information flow) in such a network. The crucial idea is to use a special class of 'geometric states' and the strength of correlations across the network, according to the intuition that, under certain conditions, quantum systems are closer the more information they have about one another. Unfortunately, the fellow was scooped on part of this. Both investigations will be completed and published this year.
Finally, the fellow finished a reconstruction of quantum theory, deriving its formalism from elementary rules governing an observer's acquisition of information about physical systems. This is a significant step forward as it allows one to understand quantum theory - normally only defined in terms of physically opaque axioms - operationally as a law book governing the act of information acquisition. This reconstruction was published in two articles in Quantum and in Phys. Rev. A. The fellow also wrote an invited review about it for a special edition of Entropy and held numerous talks elucidating it. This work, while not a main aspect of the proposal, constitutes a key aspect for motivating and justifying an informational approach to quantum gravity.
